Vibration is accompanied with all moving objects. There are frequent occasions when the vibration is not considered in designing machinery and equipment, or a structure. Due to the undesirable vibration, troubles or malfunctions are occurred, and thus additional efforts are required for restriction of the vibration. In order to reduce the vibration, it is necessary to grasp a cause of generation of the vibration, a vibration transmission path, a dynamic characteristic of the structure and the like, and the measurement of vibration is an essential element in this process. A machine under operation is unavoidably accompanied by vibration, but it is possible to detect a change in state of the machine by monitoring vibration signals, and thus the measurement of vibration is performed for the purpose of preventing and maintaining damage to the machinery and equipment, or the structure. Recently, as the structures such as a bridge and a building become larger and machine parts becomes lighter, a frequency component of the vibration is extended to low and high frequency ranges.
As the necessity for the measurement of vibration over a wide frequency range with a high degree of accuracy is increased, calibration of a vibration transducer becomes accordingly more important. However, in order to accurately measure the vibration using an accelerometer, the response characteristics of the accelerometer with respect to external vibration should be known. The accelerometer is an apparatus that transforms external vibration into electrical output. If an electrical output ratio of the accelerometer and a magnitude of the vibration applied to the accelerometer are known, then an absolute magnitude of vibration signal can be accurately measured. This characteristic is the magnitude information of accelerometer sensitivity. There is phase lag between the vibration applied to the accelerometer and the electrical output from the accelerometer, and the phase lag is phase information of the sensitivity of the accelerometer. The phase and magnitude of the sensitivity of the accelerometer is a function of the frequency.
FIG. 1 shows the phase sensitivity and the magnitude of the accelerometer. The real vibration can be reconstructed completely from the measured signal with the magnitude and the phase information of the sensitivity of the accelerometer. The sensitivity of the accelerometer is defined as a ratio of the vibration applied to the accelerometer to the electrical output from the accelerometer. The sensitivity is a complex quantity having magnitude and phase and also a function of the frequency. Calibration of the accelerometer is a process of determining the sensitivity of the accelerometer. In order to calibrate the accelerometer through primary calibration by sinusoidal excitation, the accelerometer has to be excited by a sinusoidal motion. It is first necessary to apply vibration to the accelerometer. Sinusoidal vibration can be applied to the accelerometer using an electro-dynamic exciter. The vibration of the accelerometer and the electrical output from the accelerometer should then be measured during the sinusoidal motion of the accelerometer. The vibration of the accelerometer can be measured by various methods. However, it is known that the vibration of the accelerometer can be measured most accurately using a laser interferometer. The electrical output from the accelerometer can be measured using a digital voltmeter or a spectrum analyzer.
Several methods of analyzing the laser interferometer signal can be used to accurately determine the sensitivity of the accelerometer, including a Fringe counting method, a Fringe disappearance method, a harmonic components ratio method, a sine-approximation method and the like, but only the sine-approximation method can estimate the magnitude and the phase.
The sine-approximation method can calibrate the phase and the magnitude of the sensitivity in the frequency range of 1 Hz˜10 kHz. Also, the sine-approximation method can be used to analyze the interference signal of a homodyne interferometer and a heterodyne interferometer.
The sine-approximation method with the homodyne interferometer should configure a Michelson interferometer having two quadrature signal outputs.
FIG. 2 shows an entire configuration of a measuring system using the sine-approximation method. Referring to FIG. 2, the measuring system includes a frequency generator 1, a power amplifier 2, a vibrator 3, a moving part of vibrator 4, a dummy mass 5, an accelerator 6, an amplifier 7, an interferometer 8, a laser 9, a photo-detector 10, a digital waveform recorder 11, a voltmeter 12, a distortion meter 13 and an oscilloscope 14. Since a function of each element of the measuring system is well known, the description thereof will be omitted.
The measuring system with the sine-approximation method uses two photo-detectors 10. It is important that phase difference between the output signals measured from the interferometer through the photo-detector 10 is precisely 90°.
If the phase difference between the output signals of the two photo-detectors 10 is not precisely 90°, an error may be occurred in the estimation of the phase lag in the sine-approximation method. Particularly, when a vibration displacement is less than 0.5 μm, the error may become more than 0.3°. In order to mitigate this problem, the measurement error of the quadrature output signals should be corrected.
Also, the interferometer in the sine-approximation method has a more complicated configuration than those in other methods. For example, since the sine-approximation method uses the two photo-detectors 10, a quantity of light is reduced comparing with other methods using a single photo-detector, and a signal processing procedure is complicated.
When the vibration displacement is in a nanometer range, it is recommended that the heterodyne interferometer system should be employed. However, the heterodyne interferometer system is generally more complicated than the homodyne interferometer system with respect to its configuration, and thus the manufacturing cost is increased.